I am a bit confused on the size of the SOM grid size suggested by Vesanto.
Here in this link, it says 5*sqrt(N) where N is mentioned as the dataset size. What is meant by dataset size? the number of observations (rows)? number of dimensions (columns)? or product of the two?
And here also there is a mention of it, but the instructions are not clear.
could somebody clarify what is meant by N?
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$\begingroup$ and another source is here giscience2010.org/pdfs/paper_230.pdf $\endgroup$– jackyCommented May 29, 2017 at 8:27
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$\begingroup$ Note that to attribute this info, all three of those links refer to either each other or to another Vesanto paper. Thus it seems that the 5sqrtN figure originates in the paper: "Clustering of the Self Organizing Map" (2000) scholar.google.com.au/… $\endgroup$– Tom AndersonCommented Jun 3, 2017 at 14:22
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$\begingroup$ FYI, the Vesanto (2000) paper doesn't allow searching for the 5 sqrt(N) value, but it's located on page 588. $\endgroup$– Tom AndersonCommented Jun 5, 2017 at 5:44
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1 Answer
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Given that every data sample (or row/observation) gets mapped to the winning neuron in the SOM and its influence spreaded to neighboring neurons, N has to be the number of samples.
It wouldn't make any sense for it to be the dimensionality of the samples (number of variables). Imagine the case of a simple dataset, like the Iris dataset. That would make a SOM with only four neurons, hardly useful for any subsequent task.
Remember that samples map to the winning neuron, so their format has to match between them.
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$\begingroup$ so it should be
5*sqrt(rows*colums), right? $\endgroup$– jackyCommented May 30, 2017 at 7:06 -
$\begingroup$ I think that columns are your features. If each row is one observation, then # nodes = 5 * sqrt(# rows). Kohonen has suggested a different figure of ~50 observations per node, but it's all about having a statistically significant number of observations for each node. $\endgroup$ Commented May 30, 2017 at 10:53
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$\begingroup$ Note that for visualising Iris with only 150 observations, Kohonen's rule of thumb would give only 3 nodes. That's his rule of thumb for a histogram. Google isn't showing me the pages from Vesanto's chapter, but I suppose it's just a rule of thumb that means for tiny 150 observation datsets you still get a decent sized map. It totally depends on the distribution of your data so these "rules" should be starting points only. $\endgroup$ Commented May 30, 2017 at 11:43
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2$\begingroup$ Those are only starting points. There are no absolute answers for these questions, only guides. But to sum it up, it would be 5*sqrt(observations), if you wish. Experience and personal preference should command over set-in-stone rules. Probably you want slowly transitioning zones among samples (more nodes), or perhaps, your desire is to force samples into a tight clustering-like model (less nodes). I advise you to experiment with these values and see what better fit your needs. $\endgroup$– shirowwwCommented May 30, 2017 at 13:30
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1$\begingroup$ I agree with @shirowww. Vesanto states, "N is the number of samples in the dataset." $\endgroup$ Commented Jun 3, 2017 at 14:26